Problem: You're at a clothing store that dyes your clothes while you wait. You get to pick from $4$ pieces of clothing (shirt, pants, socks, or hat) and $3$ colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?
$\text{Probability} = \dfrac{\text{Favorable combinations}}{\text{Total possible combinations}}$ There are $3$ color choices and $4$ choices for the piece of clothing, so there are $3\times4=12$ total possible combinations. If we pick randomly, all the combinations are equally likely. The red combinations are combinations that include both orange and hat. There is $1$ favorable combination. The probability of randomly picking an orange hat is $1$ out of $12$, or $\dfrac{1}{12}$.